Average Fluid Velocity Research Articles

Enhancement of Underfill Capillary Flow in Flip-Chip Packaging by Means of the Inertia Effect

This paper describes how the use of inertia forces induced by the rotation of a working disk may be adopted to increase the fill rate of the flip-chip packaging process and thereby reduce the process cycle time. It is shown how the driving forces resulting from the inertia effect are determined by the Weber number. The constant and varying contact angle models are compared under a specified set of process conditions. The calculated flow behavior results indicate that the relationship between the contact angle, the average fluid velocity, the liquid-air interface position, and the filling time depends upon the Weber number. The constant and varying contact angle models are utilized in the analysis of a new processing method referred to as rotation-enhanced underfill packaging (REUP). The inertia effect induced by the angular motion of the working disk is shown to enhance the flow of the underfill encapsulant and to reduce the time of the underfill process. The present results confirm that the rotation of the working disk leads to an increased underfill capillary flow rate, which is beneficial in reducing the production cycle time of the flip-chip packaging process.

Continuous pilot plant–scale immobilization of yeast in κ‐carrageenan gel beads

AbstractA novel continuous two‐phase dispersion process was developed to produce κ‐carrageenan gel microspheres, using static mixers. It was shown that yeast‐loaded carrageenan beads, with controlled diameter and tight size distribution, can be produced on a continuous basis, in a scalable mixer, at production rates appropriate to both pilot plant–scale and, potentially, industrial‐scale operations. Immobilized yeast are intended to be used in continuous brewing operations. The effects of the static mixer diameter (D), the number of mixing elements (Ne), the fluid linear velocity (V), and the volumetric fraction (ϵ) of κ‐carrageenan, on the mean diameter and size distribution of the resulting gel microspheres, were studied. Image analysis showed that mean diameter was strongly influenced by the average linear fluid velocity through the mixer, and by the mixer diameter. The number of mixer elements and the mixer diameter governed bead size dispersion. A productivity of 10 L h−1 of beads was attained using a 1.27‐cm‐diameter static mixer. Because the productivity is proportional to the mixer diameter squared, this process, although suited for the production of small‐size beads (down to 50 μm), would be technically and economically feasible for a large industrial immobilization process. However, because the coefficient of variability increased with mixer diameter, and thus with scale‐up, operational improvements are suggested, such as the use of smaller‐diameter mixers operating in parallel, to reduce the size dispersion. © 2004 American Institute of Chemical Engineers AIChE J, 50: 1599–1605, 2004

Triboelectrification of molten linear low-density polyethylene under continuous extrusion

The triboelectrification of molten linear low-density polyethylene under continuous extrusion through brass and stainless steel dies was studied in this work within a temperature range from 180 to 210 °C. The electric charge build-up was only observed during the extrusion through the brass die at all the temperatures studied and is attributed to slip at the die wall, namely, to a dynamic friction between the polymer melt and the die wall. The magnitude of the electric charge in the melt increased along with temperature and was dependent on the flow conditions (shear stress and sliding velocity). The electric charge exhibited a maximum for each studied temperature; the lower the temperature the lower the shear stress at which the maximum appeared. The results in this work suggest that such maxima and the further reduction in the electric charge as the shear stress is increased stem from a decrease of the contribution of slip to the average fluid velocity, because of shear thinning in the melt. Finally, friction curves were monotonic for all the temperatures and shear rates studied.

A similarity parameter for capillary flows

A similarity parameter for quasi-steady fluid flows advancing into horizontal capillary channels is presented. This parameter can be interpreted as the ratio of the average fluid velocity in the capillary channel to a characteristic velocity of quasi-steady capillary flows. It allows collapsing a large data set of previously published and recent measurements spanning five orders of magnitude in the fluid velocity, 14 different fluids, and four different geometries onto a single curve and indicates the existence of a universal prescription for such flows. On timescales longer than the characteristic time it takes for the flow to become quasi-steady, the one-dimensional momentum equation leads to a non-dimensional relationship between the similarity parameter and the penetration depth that agrees well with most measurements. Departures from that prescription can be attributed to effects that are not accounted for in the one-dimensional theory.

Determination of flow velocity vector based on Doppler shift and spectrum broadening with optical coherence tomography

We describe a technique that uses Doppler optical coherence tomography to estimate accurately the scattering fluid-flow velocity without a priori knowledge of the Doppler angle. Our technique is based on the combined use of the Doppler shift on the interference signal and the Doppler spectrum broadening caused by the particles moving across the probe beam. It is shown that the estimated values of the Doppler angle and average fluid velocity from the experiments agree well with the preset values.

Electrokinetic flow in a capillary with a charge-regulating surface polymer layer

An analytical study of the steady electrokinetic flow in a long uniform capillary tube or slit is presented. The inside wall of the capillary is covered by a layer of adsorbed or covalently bound charge-regulating polymer in equilibrium with the ambient electrolyte solution. In this solvent-permeable and ion-penetrable surface polyelectrolyte layer, ionogenic functional groups and frictional segments are assumed to distribute at uniform densities. The electrical potential and space charge density distributions in the cross section of the capillary are obtained by solving the linearized Poisson–Boltzmann equation. The fluid velocity profile due to the application of an electric field and a pressure gradient through the capillary is obtained from the analytical solution of a modified Navier–Stokes/Brinkman equation. Explicit formulas for the electroosmotic velocity, the average fluid velocity and electric current density on the cross section, and the streaming potential in the capillary are also derived. The results demonstrate that the direction of the electroosmotic flow and the magnitudes of the fluid velocity and electric current density are dominated by the fixed charge density inside the surface polymer layer, which is determined by the regulation characteristics such as the dissociation equilibrium constants of the ionogenic functional groups in the surface layer and the concentration of the potential-determining ions in the bulk solution.

Motion of a particle between two parallel plane walls in low-Reynolds-number Poiseuille flow

A new boundary-integral algorithm for the motion of a particle between two parallel plane walls in Poiseuille flow at low Reynolds number was developed to study the translational and rotational velocities for a broad range of particle sizes and depths in the channel. Instead of the free-space Green’s function more commonly employed in boundary-integral equations, we used the Green’s function for the domain between two infinite plane walls [Liron and Mochon, J. Eng. Math. 10, 287 (1976)]. This formulation allows us to directly incorporate the effects of the wall interactions into the stress tensor, without discretizing the bounding walls, and use well-established iterative methods. Our results are in good agreement with previous computations [Ganatos et al., J. Fluid Mech. 99, 755 (1980)] and limiting cases, over their range of application, with additional results obtained for very small particle–wall separations of less than 1% of the particle radius. In addition to the boundary-integral solution in the mobility formulation, we used the resistance formulation to derive the near-field asymptotic forms for the translational and rotational velocities, extending the results to even smaller particle–wall separations. The decrease in translational velocity from the unperturbed fluid velocity increases with particle size and proximity of the particle to one or both of the walls. The rotational velocity exhibits a maximum magnitude between the centerline and either wall, due to the competing influences of wall retardation and the greater fluid velocity gradient near the walls. The average particle velocity for a uniform distribution of particles was generally found to exceed the average fluid velocity, due in large part to exclusion of the particle centers from the region of slowest fluid near the walls. The maximum average particle velocity is 18% greater than the average fluid velocity and occurs for particle diameters that are 42% of the channel height; particles with diameters greater than 82% of the channel height have smaller average velocities than does the fluid, due to the retarding effects of the nearby walls. Additionally, the translational and rotational velocities of oblate and prolate ellipsoids were calculated using the boundary-integral algorithm. The proximity of the walls to the ellipsoids was found to have a strong effect on particle velocity, so that a prolate spheroid aligned on the channel centerline moves faster than an oblate spheroid of the same volume, because the edge of the latter spheroid is closer to the channel walls. For off-centerline locations for a prolate spheroid with its major axis at an angle to the walls, a second translational velocity component normal to the walls is present. For each lower-wall gap examined, the maximum normal translational velocity occurs for smaller gaps from the upper wall (i.e., larger angle). The direction of this velocity component changes sign for mid-range angles studied, due to increased interactions with the lower wall that prevent the ellipsoid from rotating upward and, hence, yield a negative velocity perpendicular to the walls. The rotational velocity changes direction for particles at the smallest angles studied, due to the competition between the Poiseuille fluid velocity profile, which pushes the particle clockwise, and the lubrication forces, which impede this rotation.

Correlations between local conversion and hydrodynamics in a 3-D fixed-bed esterification process: An MRI and lattice-Boltzmann study

In situ magnetic resonance (MR) visualisation techniques are used to study chemical conversion within a fixed-bed reactor. The reaction chosen for study is the esterification of acetic acid by methanol, catalysed by an acidic ion exchange catalyst. MR visualisation shows that fractional variations in steady-state conversion within slice sections of the bed, perpendicular to the direction of superficial flow, are of order 20%. The origin of this heterogeneity in conversion lies in the heterogeneity in the fluid flow field within the bed as is seen directly from MR flow visualisation. A lattice-Boltzmann code is validated for the prediction of the flow field within this fixed bed of porous resin packing. The lattice-Boltzmann predictions of the flow field are then used to explore any dependence of local conversion within the bed with locally averaged fluid velocity, over varying length-scales within the bed. These data report a first demonstration that MR visualisation techniques can be used to gain insight into the true rate-limiting processes influencing the performance of fixed-bed reactors.

COMPUTATIONAL FLUID DYNAMICS MODELING OF FLUID FLOW IN HELICAL TUBES

ABSTRACTThe effect of different processing parameters on the degree of mixing and axial and radial pressure drops, during single‐phase flow in helical tubes was investigated by using CFD software. Correlations were developed to calculate axial and radial pressure drops, and also the ratio of maximum to average fluid velocities. All of these quantities were found to be dependent on curvature ratio (ratio of tube diameter to coil diameter). Flow visualization experiments were performed to assess the degree of mixing in different configurations. At identical conditions, the degree of mixing was higher in the system with the large curvature ratio, which is in agreement with the simulation results. A minimum ratio of maximum to average fluid velocities of 1.61 was achieved, representing a 20% reduction in hold tube length for Newtonian fluid in laminar flow.

Electrokinetic flow velocity in charged slit-like microfluidic channels with linearized Poisson-Boltzmann field

In cases of the microfluidic channel, where the thickness of electric double layer is often comparable with the characteristic size of flow channels, the electrokinetic influence on the flow behavior can be found. The externally applied body force originating from the electrostatic interaction between the linearized Poisson-Boltzmann field and the flow-induced electrical field is applied in the equation of motion. An analytical solution to this Navier-Stokes equation of motion for well-defined geometry of slit-like microchannel is obtained by employing Green’s function. Also, an explicit analytical expression for the induced electrokinetic potential is successfully derived as functions of relevant physicochemical parameters. The effects of the ionic concentration of the fluid, the zeta potential of the solid surface, and the width of microchannels on the velocity profile as well as the streaming potential are examined. The electric double layer effect on the velocity profile becomes stronger as the channel width decreases, where the average fluid velocity is entirely reduced with the decrease in ionic concentration. The induced electrokinetic potential increases with an increase in pressure gradient, while it decreases as the ionic concentration increases.

MODELLING TWO-PHASE FLOW-EXCITED DAMPING AND FLUIDELASTIC INSTABILITY IN TUBE ARRAYS

This paper reports the results of an experimental study of the flow-induced vibration of a heat exchanger tube array subjected to two-phase cross-flow of refrigerant 11. The primary concern of the research was to develop a methodology for predicting the critical flow velocities for fluidelastic instability which better characterize the physics of two-phase flows. A new method is proposed for calculating the average fluid density and equivalent flow velocity of the two-phase fluid, using a newly developed void fraction model to account for the difference in velocity between the gas and liquid phases. Additionally, damping measurements in two-phase flow were made and compared with the data of other researchers who used a variety of modelling fluids. The results show that the two-phase damping follows a similar trend with respect to homogeneous void fraction, and when normalized, agree well with the data in the literature. The fluidelastic threshold data of several researchers who used a variety of fluids, is re-examined using the proposed void fraction model, and the results show a remarkable change in trend with flow regime. The data corresponding to the bubbly flow regime shows no significant deviation from the trend established by Connors' theory. However, the data corresponding to the intermittent flow regime show a significant decrease in stability which is nearly independent of the mass-damping parameter. It is believed that the velocity fluctuations that are inherent in the intermittent flow regime are responsible for tripping the instability, causing lower than expected stability of the bundle.

Analog signal processing in an AC electromagnetic flowmeter

AC electromagnetic flowmeters yield a low-frequency signal whose amplitude is proportional to the average fluid velocity. Typically, the input signal magnitude is below 1 mV and suffers a strong electric and magnetic interference from the coils that create the driving magnetic field. This paper provides a novel circuit design to amplify and demodulate the voltage picked up by the electrodes and to minimize interference. The amplifier includes a fully differential front end. The demodulation consists of synchronous rectification and sampling with zero-order hold followed by low-pass filtering. The result is a 0.25-mV/(m/s)/mT voltage, insensitive to DC level shifts.

Diffusion and advection within and around sinking, porous diatom aggregates

Fluid motion within and around sinking aggregates is an important factor in particle scavenging and solute exchange between sinking aggregates and the surrounding water and, hence, vertical fluxes and remineralization processes in the ocean. In the present study, we analyzed O2 uptake rates in >2‐mm porous diatom aggregates and in model aggregates impermeable to flow by measuring, on the same aggregates, the interface diffusive uptake rates with microsensors and the total (diffusive + advective) O2 uptake rate by the Winkler method. The uptake rates were measured in a flow field similar to that experienced by sinking aggregates. The ratio of total O2 uptake rate to diffusive uptake rate was 0.97 ± 0.10 (n = 14) in model aggregates impermeable to flow. In contrast, total O2 uptake was similar to or higher than diffusive uptake rate calculated from the O2 gradients at the aggregate‐water interface in 85% of all field‐sampled and roller tank diatom aggregates examined. The highest ratio of total O2 uptake rate relative to diffusive uptake rate measured in <1‐cm field‐sampled diatom aggregates was 3.91 ± 1.39 (n = 22). Hence, diffusive O2 uptake calculated from the O2 gradients in aggregates is a conservative (minimum) estimate of total O2 uptake. The estimated average fluid velocity through the cross‐sectional area of field‐sampled diatom aggregates, which could explain the measured differences in O2 uptake, ranged between 5 and 40 µm s-1. The average value was 16 µm s-1, which was equal to 1.3% of aggregate sinking velocity.

Quantification of the slip phenomenon and the effect of shear thinning in the capillary flow of linear polyethylenes

AbstractThe slip phenomenon in the capillary flow of linear polyethylenes and its relation to their shear‐thinning behavior was studied in this work. A simple macroscopic analysis that allows a description of the trend of the slip length and the contribution of slip to the average fluid velocity as functions of the shear stress is presented. From this analysis it is shown that an increase or decrease of the slip length for increasing shear stress is determined by the polymer architecture and the competition between slip and shear thinning. A similar behavior is observed for the ratio between the slip and whole average fluid velocities. The analysis is validated using experimental data obtained during the continuous extrusion of linear low‐density polyethylene melts under strong slip conditions in a brass die.

Velocity of isolated particles along a pipe in stratified gas–liquid flow

AbstractThe average velocity of isolated grains of sand was experimentally measured in smooth stratified flow in slightly declined pipes. Isolated particles in smooth stratified flow behave similarly to isolated particles propelled by both hydraulic conveying and intermittent gas/liquid flow. In all three cases, particle velocity is linear with respect to the average liquid velocity of the flow (or the average fluid velocity in the slug body for intermittent flow) and has a gradient of approximately one. The data in stratified flow are successfully correlated dimensionlessly (Eq. 7). The correlation is extrapolated to zero particle velocity to estimate the conditions required to ensure sand transport in a flowline in smooth stratified flow. The experimental results suggest that particle velocity is strongly governed by the size of a particle relative to the depth of the viscous sublayer at the pipe wall. If a particle is larger than the viscous sublayer, it is exposed to more coherent turbulent structures and therefore experiences a greater drag.

Axial development and radial non-uniformity of flow in packed columns

Flow inhomogeneity and axial development in low-pressure chromatographic columns have been studied by magnetic resonance imaging velocimetry. The columns studied included (a) an 11.7-mm I.D. column packed with either 50 μm diameter porous polyacrylamide, or 99 or 780 μm diameter impermeable polystyrene beads, and (b) a 5-mm I.D. column commercially packed with 10 μm polymeric beads. The packing methods included gravity settling, slurry packing, ultrasonication, and dry packing with vibration. The magnetic resonance method used averaged apparent fluid velocity over both column cross-sections and fluid displacements greater than one particle diameter and hence permits assessment of macroscopic flow non-uniformities. The results confirm that now non-uniformities induced by the conical distributor of the 11.7-mm I.D. column or the presence of voids at the column entrance relax on a length scale of the column radius. All of the 11.7-mm I.D. columns examined exhibit near wall channeling within a few particle diameters of the wall. The origins of this behavior are demonstrated by imaging of the radial dependence of the local porosity for a column packed with 780 μm beads. Columns packed with the 99-μm beads exhibit reduced flow in a region extending from ten to three-to-five particle diameters from the wall. This velocity reduction is consistent with a reduced porosity of 0.35 in this region as compared to approximately 0.43 in the bulk of the column. Ultrasonicated and dry-packed columns exhibit enhanced flow in a region located between approximately eight and 20 particle diameters from the wall. This enhancement maybe caused by packing density inhomogeneity and/or particle size segregation caused by vibration during the packing process. No significant non-uniformities on length scales of 20 μm or greater were observed in the commercially packed column packed with 10 μm particles.

Experimental and Numerical Analysis of Turbulent Opposed Impinging Jets

A fundamental study of two turbulent, directly opposed impinging jets in a stagnant ambient fluid, unconfined or uninfluenced by far-field walls, is presented. By experimental investigation and numerical modeling the fundamental characteristics of direct impingement of two turbulent axisymmetric round jets under seven different geometrical and flow-rate configurations (L * = L/d = {5, 10, 20}, where L is nozzle to nozzle separation distance and d is nozzle diameter, and Re = ρU 0 d/μ = {1500, 4500, 7500, 11000}, where ρ is fluid density, μ is dynamic viscosity of fluid, and U 0 is average initial velocity of fluid) are discussed. Flow visualization and velocity measurements performed using various laser-based techniques have revealed the effects of Reynolds number Re and dimensionless nozzle to nozzle separation L * on the complex flow structure. Similarity analysis of the initial freejet development and developing radial jet found Re = 11 x 10 3 and L * = 20 as the only case where the freejets exhibit a self-preserving development

Magnetohydrodynamic Stability of Two Streaming Superposed Viscoelastic Conducting Fluids

Abstract The stability of the plane interface separating two Oldroydian viscoelastic superposed moving fluids of uniform densities when immersed in a uniform horizontal magnetic field has been in­ vestigated. The stability analysis has been carried out, for mathematical simplicity, for two highly viscous fluids of equal kinematic viscosities. It is found that the potentially stable configuration remains stable if the fluids are at rest, while it becomes unstable if the fluids move. The stability criterion is found to be independent of the viscosity and viscoelasticity, and to be dependent on the orientation of the magnetic field and the magnitudes of the fluids and Alfven velocities. It is also found that the potentially unstable configuration remains unstable in the absence of average fluid velocities, or in the presence of fluid velocities and absence of a magnetic field. The magnetic field is found to stabilize a certain wavenumbers range of the unstable configuration even in the presence of the effects of viscoelasticity. The behaviour of growth rates with respect to the stress relaxation time, strain retardation time, fluid and Alfven velocity parameters is examined analytically, and the stability conditions are obtained and discussed. -Pacs: 47.20.-k; 47.50.+d; 47.65.+a.

Effect of fracture roughness on solute transport

The purposes of this study are to investigate how fracture roughness affects solute transport and is to find a better transport mechanism causing a long breakthrough tailing. To achieve the purposes, the lattice Boltzmann method was used for simulating the solute transport in rough fractures. Rougher fracture yields a large velocity gradient across the aperture, especially at high average fluid velocity (Re>20). Consequently, solute transports fast in the middle of the aperture, and a significant fraction of solute are delayed and transport slowly along the fracture wall, which can be described as the “film” transport. This “film” transport results in high solute dispersion, and was found to be a better explanation for a long tailing in the breakthrough curve, rather than the most common explanation for a long tailing, the diffusive exchange of solutes between mobile and immobile fluids. As long as fluid velocity is kept small, discrepancy between tracer and hydraulic apertures may not be significant, regardless of fracture roughness.

Experimental Verification of Two New Theories Predicting Temperature-Dependent Viscosity Effects on the Forced Convection in a Porous Channel

Experimental Verification of Two New Theories Predicting Temperature-Dependent Viscosity Effects on the Forced Convection in a Porous Channel